Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Abstract

Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form F(\Phi) (\nabla\Phi)^4F(Φ)(∇Φ)4 in a class of string vacua known as CHL \IZ_N heterotic orbifolds with NN prime, generalizing our previous work which dealt with the case of heterotic string on T^6T6. We derive the Ward identities that F(\Phi)F(Φ) must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of F(\Phi)F(Φ), and show that it reproduces the correct tree-level and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact F^4F4 coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in D=4D=4 and D=3D=3, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.